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Curvatures and Tolerances in the Euclidean Motion Group

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Abstract

We investigate the action of imprecisely defined affine and Euclidean transformations and compute tolerance zones of points and subspaces. Tolerance zones in the Euclidean motion group are analyzed by means of linearization and bounding the linearization error via the curvatures of that group with respect to an appropriate metric.

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Authors and Affiliations

  1. Institut für Technische Mathematik, Geometrie und Bauinformatik, Universität Innsbruck, Technikerstra\e 13, A 6020, Innsbruck, Austria

    Hans-Peter Schröcker

  2. Institut für Diskrete Mathematik und Geometrie, Technische Universität Wien, Wiedner Hauptstra\e 8-10/104, A 1040, Wien, Austria

    Johannes Wallner

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  1. Hans-Peter Schröcker
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  2. Johannes Wallner
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Correspondence to Hans-Peter Schröcker.

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Schröcker, HP., Wallner, J. Curvatures and Tolerances in the Euclidean Motion Group. Results. Math. 47, 132–146 (2005). https://doi.org/10.1007/BF03323019

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